Question

Find an equation of the tangent plane to the given surface at the specified point (2,-1,-3)

for

z =3y^(2) - 2x^(2) + x

Answer 1

First we need to take partial derivatives

Answer 2

Have you learned these

Answer 3

yes I know how to take partial derivatives

Answer 4

\[f_{x} = -4x +1\]
\(f_{y} = 6y\)

Answer 5

yes that is what I have gotten

Answer 6

sweet

Answer 7

is the formula

z-z_0 = f_x(x,y)(x-a) + f_y(x,y)(y-a)?

Answer 8

I assume it is not

Answer 9

No you are correct!
\[f_{x}(x_{0},y_{0})(x−x_{0})+f_{y}(x_{0},y_{0})(y−y_{0})−(z−z_{0})=0\]

Answer 10

\(x_{0} = 2\)
\(y_{0} = -1\)
\(z_{0} = 3\)

Answer 11

For the functions just plug in \(x_{0}\) and \(y_{0}\) into the partials.

Answer 12

I got:
\[-7(x−2)-6(y+1)−(z−3)=0\]

Answer 13

you could simplify i suppose..

Answer 14

oh I see thanks

Answer 15

no problem... kind of a silly formula to have to memorize.. i suppose you could learn to derive it but i never did lol

Answer 16

well it is similar to

f'(x)(x-a) + f(x) = y

from calc 1

Answer 17

so its not that hard to remember